【目的】无刷直流(BLDC)电机的多目标优化通常依赖于大量的有限元分析,不仅计算成本高昂,而且耗时。虽然代理模型能够加速设计过程,但传统的数据驱动模型在物理边界附近的预测往往失真,导致输出值不具有物理意义。针对这个问题,本文提出一种基于物理约束改进高斯过程回归(GPR)与置信下限(LCB)的鲁棒优化方法。【方法】首先,采用基于Campolongo策略的改进 Morris 轨迹采样法对电机关键结构参数进行全局敏感度分析,实现设计变量的降维筛选。其次,针对电机效率和转矩脉动的物理特性,在 GPR 建模中引入对数(Log)和逻辑斯谛(Logit)变换,构建满足物理边界约束的高精度代理模型。最后,利用 GPR 提供的预测方差信息进行不确定性量化,提出基于LCB的稳健优化策略,通过两阶段搜索在提升电机综合性能的同时,有效增强设计方案的工程稳健性。【结果】所提出的框架在验证过程中表现卓越。改进的GPR模型在数学上消除了电机效率和转矩脉动边界处的非物理预测,与传统替代模型相比,显著提高了测试集上的泛化精度。当应用于无刷直流电机设计时,最终优化方案表现出了显著的提升。具体而言,输出转矩提高了9.56%,转矩脉动大幅降低了47.18%。同时,电机整体效率可靠地保持在90%以上。【结论】该方法有效解决了无刷直流电机优化中存在的计算瓶颈和模型预测失真问题。通过在建模架构中结构化地整合物理约束,并利用不确定性感知的置信下限策略,所提出的方法在全面提高电磁性能的同时,有效增强了设计方案的工程稳健性和实际可行性。

[Objective] The multi-objective optimization of brushless direct current (BLDC) motors frequently relies on extensive finite element analysis, which is computationally expensive and time-consuming. While surrogate models accelerate the design process, traditional data-driven models often suffer from prediction distortion near physical boundaries, resulting in non-physical output values. To address this issue, this paper proposes a novel robust optimization methodology integrating a physically constrained gaussian process regression (GPR) model with a lower confidence bound (LCB) strategy. [Methods] Firstly, an improved Morris trajectory sampling method based on the Campolongo strategy was adopted to perform global sensitivity analysis on the key structural parameters of the motor, and achieved dimensionality reduction and screening of design variables. Secondly, considering the physical characteristics of motor efficiency and torque ripple, logarithmic (Log) and logistic (Logit) transformations were introduced into the GPR modeling to construct a high-accuracy surrogate model that satisfied physical boundary constraints. Finally, uncertainty quantification was performed using the predictive variance information provided by GPR, and a robust optimization strategy based on LCB was proposed. Through a two-stage search, the comprehensive performance of the motor was improved, while the engineering robustness of the design scheme was effectively enhanced. [Results] The proposed framework demonstrated excellent performance during validation. The improved GPR model mathematically eliminated non-physical predictions at the boundaries of motor efficiency and torque ripple, and it achieved significantly higher generalization accuracy on the test set compared with conventional surrogate models. When applied to the design of the BLDC motor, the final optimized design exhibited substantial improvements. Specifically, the output torque was increased by 9.56%, and the torque ripple was dramatically reduced by 47.18%. Meanwhile, the overall motor efficiency was reliably maintained above 90%. [Conclusion] This method effectively addresses the computational bottlenecks and model prediction distortions present in BLDC motor optimization. By structurally integrating physical constraints within the modeling architecture and utilizing the uncertainty-aware LCB strategy, the proposed method comprehensively improves electromagnetic performance while effectively enhancing the engineering robustness and practical viability of the design scheme.

国家自然科学基金青年科学基金项目（52207041）